Multi-beam scanning device, multi-beam scanning method, light source device, and image forming apparatus

ABSTRACT

In a multi-beam scanning device and method of the present invention, a semiconductor laser array having a plurality of light emitting parts emitting multiple laser beams is provided. A rotary deflector deflects the laser beams emitted by the light emitting parts of the semiconductor laser array. The deflected laser beams from the rotary deflector is focused onto a scanned surface to form a plurality of beam spots that are separated on the scanned surface in a sub-scanning direction, the scanned surface being scanned simultaneously with the plurality of beam spots in a main scanning direction by a rotation of the rotary deflector. The laser array is configured such that the light emitting parts are arrayed along a line that is at an inclination angle φ to the sub-scanning direction, the inclination angle φ measured in degrees and meeting the conditions 0≦φ&lt;90, and that a scanning line pitch P, an array pitch ρ of the light emitting parts of the laser array and a parameter K defined by the equation 
     
       
           K= 0.82λ/ω z,   
       
     
     where λ is a wavelength of the emitted laser beams and ωz is a target beam spot diameter in the sub-scanning direction, satisfy the following conditions: 
     
       
         0.01&lt; K·P /(ρ·cos φ)&lt;0.30 
       
     
     
       
         0.011&lt; K &lt;0.030.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a multi-beam scanning device, amulti-beam scanning method, and a light source device for use in themulti-beam scanning device. Further, the present invention relates to animage forming apparatus in which the multi-beam scanning device isprovided.

2. Description of the Related Art

With the widespread use of image forming apparatus, such as laserprinters and digital copiers, there is an increasing demand for improvedprinting speeds of the image forming apparatus. To meet the requirement,a multi-beam scanning device having a plurality of light sources isproposed for use in the image forming apparatus. In the multi-beamscanning device, the plurality of light sources, such as laser diodes,are used to emit multiple light beams for scanning the scanned surfacewith the multiple light spots at a time. For example, a multi-beamscanning device using a semiconductor laser array as the plurality oflight sources is known.

When the optical scanning is performed on a scanned surface of aphotosensitive medium at a higher density (e.g., above 600 dpi) with themulti-beam scanning device, the pitch of the scanning lines is decreasedto a smaller level to achieve the high-density scanning, and thediameter of beam spots on the photosensitive medium surface in thesub-scanning direction must be decreased accordingly. A beam spot isformed on the scanned surface by the focused laser beam from the lightsource. The scanned surface that is actually scanned with the focusedlaser beam does not necessarily accord with an image surface where thebeam spot is precisely formed at the waist of the laser beam due to thefield curvature of the focusing lens or the like of the optical scanningdevice. The diameter of the beam spot on the scanned surface is notnecessarily equal to the beam waist diameter. To reduce the variation ofthe beam spot diameter as much as possible, the correction of the fieldcurvature of the focusing lens is carried out.

Further, optical scanning devices after assembly contain several kindsof errors, regardless of whether they are the multi-beam scanning deviceor the single-beam scanning device. Such errors include respectiveerrors of the component parts of the optical scanning device, anassembly error of the optical scanning device, and others. When sucherrors exist in the optical scanning device, the beam spot formed on thescanned surface with the light beam from the optical scanning device isin a defocus state. The scanned surface that is actually scanned withthe focused laser beam is liable to variations of the image surface.

By taking the above matters into consideration, it is necessary that thedesigning of a multi-beam scanning device be based on the assumptionthat the beam spot on the scanned surface is in a defocus state. In mostcases, the multi-beam scanning device is designed such that thevariations of the beam spot diameter fall within a range of ±10% of atarget beam spot diameter “W”. Namely, the beam spot diameter, which isprovided by the multi-beam scanning device, is in a range from 0.9 W to1.1 W, where W is a target beam spot diameter.

When the beam spot on the scanned surface is in a defocus state, thebeam spot diameter is larger than the beam waist diameter. In designingthe optical systems of the multi-beam scanning device, the practicalmeasure is to determine a permissible beam spot diameter that is smallerthan the target beam spot diameter by 1 to 10 percents. A range of thedefocus amount in which the variations of the beam spot diameter areless than the above-mentioned permissible beam spot diameter is called adepth clearance. When the depth clearance is large, the degree ofallowance for the variations of the scanned surface to the image surfaceis high. It is known from practical experience that the depth clearancethat is above 0.9 mm is needed to eliminate the component part errors orthe assembly errors.

Moreover, in the conventional multi-beam scanning device, the divergenceangle of laser beams emitted by the semiconductor laser array is liableto variations. Generally, a semiconductor laser as in the semiconductorlaser array emits a divergent laser beam. The divergence angle is at themaximum in the direction of thickness of the activated layer of thesemiconductor laser and at the minimum in the direction perpendicular tothe activated layer. The far-field pattern of such laser beam is in theform of an ellipse having a major axis parallel to the direction ofthickness of the activated layer. In the semiconductor laser arraydescribed above, the respective divergence angles of the laser beamsemitted by the plurality of light emitting parts are not common, and thedivergence angle for each of the plurality of light emitting parts isliable to variations. Hence, the diameters of beam spots, which areformed on the scanned surface by the conventional multi-beam scanningdevice, are also liable to variations due to the variations of thedivergence angles. This causes the degradation of the quality of areproduced image.

SUMMARY OF THE INVENTION

In order to overcome the above-described problems, it is an object ofthe present invention to provide a multi-beam scanning device thatensures adequate depth clearance even when the optical scanning isperformed at a high density above 600 dpi, and effectively reduces thevariations of the beam spots on the scanned surface to a smallestpossible level so that the multi-beam scanning is carried out withaccurate beam spot diameter so as to create good quality of a reproducedimage.

Another object of the present invention is to provide a multi-beamscanning method that ensures adequate depth clearance even when theoptical scanning is performed at a high density above 600 dpi, andeffectively reduces the variations of the beam spots on the scannedsurface to a smallest possible level so that the multi-beam scanning iscarried out with accurate beam spot diameter so as to create goodquality of a reproduced image.

Another object of the present invention is to provide a light sourcedevice for use in a multi-beam scanning device that ensures adequatedepth clearance even when the optical scanning is performed at a highdensity above 600 dpi, and effectively reduces the variations of thebeam spots on the scanned surface to a smallest possible level so thatthe multi-beam scanning is carried out with accurate beam spot diameterso as to create good quality of a reproduced image.

Another object of the present invention is to provide an image formingapparatus in which a multi-beam scanning device is provided, themulti-beam scanning device ensuring adequate depth clearance even whenthe optical scanning is performed at a high density above 600 dpi, andeffectively reducing the variations of the beam spots on the scannedsurface to a smallest possible level so that the multi-beam scanning iscarried out with accurate beam spot diameter so as to create goodquality of a reproduced image.

The above-mentioned objects of the present invention are achieved by amulti-beam scanning device comprising: a semiconductor laser array whichhas a plurality of light emitting parts emitting multiple laser beams; arotary deflector which deflects the laser beams emitted by the lightemitting parts of the semiconductor laser array; and a focusing opticalsystem which focuses the deflected laser beams from the rotary deflectoronto a scanned surface to form a plurality of beam spots that areseparated on the scanned surface in a sub-scanning direction, thescanned surface being scanned simultaneously with the plurality of beamspots in a main scanning direction by a rotation of the rotarydeflector, wherein the laser array is configured such that the lightemitting parts are arrayed along a line that is at an inclination angleφ to the sub-scanning direction, the inclination angle φ measured indegrees and meeting the conditions 0≦φ<90, and that a scanning linepitch P, an array pitch ρ of the light emitting parts of the laser arrayand a parameter K defined by the equation

K=0.82λ/ωz,

where λ is a wavelength of the emitted laser beams and ωz is a targetbeam spot diameter in the sub-scanning direction, satisfy the followingconditions:

0.01<K·P/(ρ·cos φ)<0.30

0.011<K<0.030.

The above-mentioned objects of the present invention are achieved by amulti-beam scanning method that comprising the steps of: providing asemiconductor laser array having a plurality of light emitting partsemitting multiple laser beams; providing a rotary deflector deflectingthe laser beams emitted by the light emitting parts of the semiconductorlaser array; focusing the deflected laser beams from the rotarydeflector onto a scanned surface to form a plurality of beam spots thatare separated on the scanned surface in a sub-scanning direction; andscanning the scanned surface simultaneously with the plurality of beamspots in a main scanning direction by a rotation of the rotarydeflector, wherein the laser array is configured such that the lightemitting parts are arrayed along a line that is at an inclination angleφ to the sub-scanning direction, the inclination angle φ measured indegrees and meeting the conditions 0≦φ<90, and that a scanning linepitch P, an array pitch ρ of the light emitting parts of the laser arrayand a parameter K defined by the equation

K=0.82λ/ωz,

where λ is a wavelength of the emitted laser beams and ωz is a targetbeam spot diameter in the sub-scanning direction, satisfy the followingconditions:

0.01<K·P/(ρ·cos φ)<0.30

0.011<K<0.030.

The above-mentioned objects of the present invention are achieved by alight source device for use in a multi-beam scanning device, the lightsource device comprising: a semiconductor laser array which has aplurality of light emitting parts emitting multiple laser beams; acoupling lens which couples the laser beams emitted by the laser array;and an aperture stop which restricts a diameter of the laser beamspassed through the coupling lens, wherein the multi-beam scanning devicecomprises: the light source device; a rotary deflector which deflectsthe laser beams emitted by the light emitting parts of the laser array;and a focusing optical system which focuses the deflected laser beamsfrom the rotary deflector onto a scanned surface to form a plurality ofbeam spots that are separated on the scanned surface in a sub-scanningdirection, the scanned surface being scanned simultaneously with theplurality of beam spots in a main scanning direction by a rotation ofthe rotary deflector, wherein the laser array is configured such thatthe light emitting parts are arrayed along a line that is at aninclination angle φ to the sub-scanning direction, the inclination angleφ measured in degrees and meeting the condition 0≦φ<90, and that ascanning line pitch P, an array pitch ρ of the light emitting parts ofthe laser array and a parameter K defined by the equation

K=0.82λ/ωz,

where λ is a wavelength of the emitted laser beams and ωz is a targetbeam spot diameter in the sub-scanning direction, satisfy the followingconditions:

0.01<K·P/(ρ·cos φ)<0.30

0.011<K<0.030

and wherein the aperture stop is configured to have a numerical apertureNAzS in the sub-scanning direction that satisfies the conditions:0.01<NAzS<0.30.

The above-mentioned objects of the present invention are achieved by animage forming apparatus in which a multi-beam scanning device isprovided, the image forming apparatus forming an electrostatic latentimage on a scanned surface of a photosensitive medium through anexposure of the photosensitive medium to an imaging light patternprovided by the multi-beam scanning device, the multi-beam scanningdevice including: a semiconductor laser array which has a plurality oflight emitting parts emitting multiple laser beams; a rotary deflectorwhich deflects the laser beams emitted by the light emitting parts ofthe semiconductor laser array; and a focusing optical system whichfocuses the deflected laser beams from the rotary deflector onto ascanned surface to form a plurality of beam spots that are separated onthe scanned surface in a sub-scanning direction, the scanned surfacebeing scanned simultaneously with the plurality of beam spots in a mainscanning direction by a rotation of the rotary deflector, wherein thelaser array is configured such that the light emitting parts are arrayedalong a line that is at an inclination angle φ to the sub-scanningdirection, the inclination angle φ measured in degrees and meeting theconditions 0<φ<90, and that a scanning line pitch P, an array pitch ρ ofthe light emitting parts of the laser array and a parameter K defined bythe equation

K=0.82λ/ωz,

where λ is a wavelength of the emitted laser beams and ωz is a targetbeam spot diameter in the sub-scanning direction, satisfy the followingconditions:

0.01<K·P(ρ·cos φ)<0.30

0.011<K<0.030.

In the multi-beam scanning device and method of the present invention,the semiconductor laser array is used as the plurality of light sourcesand it is possible to ensure adequate depth clearance when the opticalscanning is performed at a high density. The multi-beam scanning deviceand method of the present invention are effective in reducing thevariations of the beam spots on the scanned surface, so that themulti-beam scanning is carried out with accurate beam spot diameter soas to create good quality of a reproduced image. Therefore, the imageforming apparatus in which the multi-beam scanning device of the presentinvention is provided can create good quality of a reproduced image.

BRIEF DESCRIPTION OF THE DRAWINGS

Other objects, features and advantages of the present invention will beapparent from the following detailed description when read inconjunction with the accompanying drawings.

FIG. 1 is a perspective view of one preferred embodiment of themulti-beam scanning device of the present invention.

FIG. 2 is a diagram for explaining a sub-scanning-direction imagingpattern of a light beam between one of the light emitting parts of alight source unit and the scanned surface of a photosensitive medium.

FIG. 3A, FIG. 3B, FIG. 3C and FIG. 3D are diagrams for explaining arelationship between the semiconductor laser array, the aperture stop,and the far-field pattern.

FIG. 4 is a diagram for explaining a configuration of the opticalsystems of a first preferred embodiment of the multi-beam scanningdevice.

FIG. 5A and FIG. 5B are diagrams for explaining the relationship betweenthe defocus amount and the spot diameter in the multi-beam scanningdevice of FIG. 4.

FIG. 6 is a diagram for explaining a configuration of the opticalsystems of a second preferred embodiment of the multi-beam scanningdevice.

FIG. 7A and FIG. 7B are diagrams for explaining the relationship betweenthe defocus amount and the spot diameter in the multi-beam scanningdevice of FIG. 6.

FIG. 8 is a diagram for explaining a configuration of the opticalsystems of a third preferred embodiment of the multi-beam scanningdevice.

FIG. 9A and FIG. 9B are diagrams for explaining the relationship betweenthe defocus amount and the spot diameter in the multi-beam scanningdevice of FIG. 8.

FIG. 10 is a diagram for explaining a configuration of the opticalsystems of a fourth preferred embodiment of the multi-beam scanningdevice.

FIG. 11A and FIG. 11B are diagrams for explaining the relationshipbetween the defocus amount and the spot diameter in the multi-beamscanning device of FIG. 10.

FIG. 12A and FIG. 12B are diagrams for explaining a configuration of theoptical systems of a fifth preferred embodiment of the multi-beamscanning device.

FIG. 13A and FIG. 13B are diagrams for explaining the relationshipbetween the defocus amount and the spot diameter in the multi-beamscanning device of FIG. 12A and FIG. 12B.

FIG. 14 is a diagram for explaining a configuration of the opticalsystems of a sixth preferred embodiment of the multi-beam scanningdevice.

FIG. 15A and FIG. 15B are diagrams for explaining the relationshipbetween the defocus amount and the spot diameter in the multi-beamscanning device of FIG. 14.

FIG. 16 is a diagram for explaining one preferred embodiment of theimage forming apparatus of the present invention.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

A description will be given of preferred embodiments of the multi-beamscanning device and the image forming apparatus of the present inventionwith reference to the accompanying drawings.

FIG. 1 is a perspective view of one preferred embodiment of themulti-beam scanning device of the present invention.

The multi-beam scanning device of the present embodiment is provided foruse in an image forming apparatus, such as a laser printer, a digitalcopier or a laser facsimile. In the image forming apparatus, an image isformed on a scanned surface of a photosensitive medium when thephotosensitive medium surface is scanned in a main scanning directionand a sub-scanning direction by the laser beams focused by themulti-beam scanning device.

Specifically, the multi-beam scanning device of the present embodimentis provided for use in an image forming apparatus that forms an imagethrough an electrophotographic printing process. In theelectrophotographic printing process, there are basically six majorsteps employed: (1) charging of the photosensitive medium; (2) exposingof the photosensitive medium to the imaging light pattern; (3)developing of the photosensitive medium with toner; (4) transferring ofthe toned image from the photosensitive medium to the final medium(usually paper); (5) thermal fusing of the toner to the paper; and (6)cleaning of residual toner from the photosensitive medium surface. Theoptical scanning of the photosensitive medium surface, which isperformed by the laser beams from the multi-beam scanning device of theabove-described embodiment, corresponds to the exposing step of theelectrophotographic printing process that is carried out by the imageforming apparatus.

As shown in FIG. 1, the multi-beam scanning device of the presentembodiment generally comprises a semiconductor laser diode (or a lightsource unit) 1, a coupling lens 2, an aperture stop 3, a line focusinglens 4, a rotary polygonal mirror 5, an fθ lens 6, an elongated focusinglens 7, a reflector mirror 8, a photosensitive belt 9, and a syncmonitoring detector. The sync monitoring device includes a mirror 10, afocusing lens 11 and a sync monitoring sensor 12. The sync monitoringsensor 12 is formed by, for example, a photodiode, and the syncmonitoring sensor 12 converts the incident light beam into a sync signalthat is indicative of a time the sync monitoring sensor 12 has receivedthe light beam from the light source unit 1.

The light source device according to one embodiment of the presentinvention is constituted by the semiconductor laser array 1, thecoupling lens 2, and the aperture stop 3 in the multi-beam scanningdevice of FIG. 1. The light source device may be configured into asingle device that includes the elements 1, 2 and 3 of the multi-beamscanning device of FIG. 1.

In the multi-beam scanning device of FIG. 1, the semiconductor laserarray 1 includes a plurality of light emitting parts that emit aplurality of divergent laser beams in accordance with an image signal(which carries imaging information). The laser beams from thesemiconductor laser array 1 are directed to the coupling lens 2. Thecoupling lens 2 couples the laser beams emitted by the semiconductorlaser array 1, and introduces the coupled laser beams into the aperturestop 3. The aperture stop 3 restricts the diameter of the incident laserbeams to an appropriate level, and introduces the laser beams into theline focusing lens 4.

The line focusing lens 4 provides a refraction power to the laser beams,passed through the aperture stop 3, with respect to only thesub-scanning direction. The line focusing lens 4 is formed by, forexample, a cylindrical lens. With the refraction power of the focusinglens 4, the laser beams from the aperture stop 4 form line images at anadjacent position of the rotary polygonal mirror 5, which are elongatedin the main scanning direction and separated from each other in thesub-scanning direction.

The rotary polygonal mirror 5 in the present embodiment is a rotarydeflector having reflection surfaces on the six peripheral sides. One ofthe reflection surfaces of the rotary polygonal mirror 5 deflects thelaser beams from the focusing lens 4 while the rotary polygonal mirror 5is rotated at a constant speed around its rotation axis in the rotationdirection indicated by the arrow in FIG. 1, which allows the scannedsurface to be scanned at a constant speed in the main scanning directionwith the beam spots.

The deflected laser beams from the polygonal mirror 5 are passed throughthe fθ lens 6 and the elongated focusing lens 7, and the laser beamsfrom the focusing lens 7 are reflected to the photosensitive belt 9 bythe reflector mirror 8. The fθ lens 6 and the elongated focusing lens 7form a focusing optical system in the multi-beam scanning device of thepresent embodiment. With the rotation of the rotary deflector 5, thelaser beams from the reflector mirror 8 scan a scanned surface of thephotosensitive belt 9 in the main scanning direction. This main scanningdirection is parallel to the axial direction of a transport roller thatis provided to rotate or transport the photosensitive belt 9 around therotation axis of the transport roller.

In a synchronous manner with a time the main scanning is performed (orevery time the laser beams from the rotary deflector 5 are incident tothe sync monitoring device), the photosensitive belt 9 is rotated aroundthe rotation axis of the transport roller by a given rotational angle.This causes the photosensitive medium surface to be scanned in thesub-scanning direction by the laser beams focused by the multi-beamscanning device. The sub-scanning direction, which is parallel to thedirection in which the photosensitive belt 9 is transported, isperpendicular to the axial direction of the transport roller of thephotosensitive belt 9. Therefore, the photosensitive medium surface isscanned in the main scanning direction and in the sub-scanning directionby the laser beams focused by the multi-beam scanning device. Each ofthe respective light emitting parts of the semiconductor laser array 1is independently turned on and off in accordance with the image signal,and an electrostatic latent image is formed on the photosensitive mediumsurface as a result of the exposure of the photosensitive belt 9 to theimaging light pattern provided by the semiconductor laser array 1.

In the multi-beam scanning device of FIG. 1, the semiconductor laserarray 1 includes the plurality of light-emitting parts that areindependently turned on and off in accordance with the image signal. Thelaser beams emitted by the light emitting parts of the semiconductorlaser array 1 are focused on the photosensitive medium surface so thatthe respective light spots are formed thereon. The photosensitive mediumsurface is scanned at a substantially constant speed in the mainscanning direction by the laser beams, focused by the multi-beamscanning device, with the rotation of the rotary deflector 5.

The coupling lens 2 may be configured to convert the laser beams emittedby the semiconductor laser array 1 into substantially parallel laserbeams. Alternatively, the coupling lens 2 may be configured to convertthe laser beams emitted by the semiconductor laser array 1 into lessdivergent laser beams. Alternatively, the coupling lens 2 may beconfigured to convert the laser beams emitted by the semiconductor laserarray 1 into convergent laser beams.

In the multi-beam scanning device of FIG. 1, the sync monitoring deviceis provided to synchronize the timing of a start of every main scanningof the photosensitive medium surface. As described above, every time thelaser beams from the rotary deflector 5 are incident to the syncmonitoring sensor 12, the sync monitoring sensor 12 outputs a syncsignal, and this sync signal is used to start the main scanning of themulti-beam scanning device.

The sync monitoring device in the present embodiment includes the mirror10, the focusing lens 11 and the sync monitoring sensor 12. The mirror10 reflects the laser beams, which are sent by the rotary deflector 5through the fθ lens 6, to the focusing lens 11. The focusing lens 11converts the laser beams into convergent laser beams and introduces theminto the sync monitoring sensor 12. The sync monitoring sensor 12 isformed by a photodiode or a charge-coupled device, and the syncmonitoring sensor 12 outputs a sync signal upon the receiving of thelaser beams from the rotary deflector 5. The photosensitive belt 9 isrotated around the rotation axis by the given rotational angle insynchronism with the sync signal output by the sync monitoring sensor12.

In the multi-beam scanning device of FIG. 1, the semiconductor laserarray 1 is provided as the light source unit that emits a plurality oflaser beams. The semiconductor laser array 1 includes a plurality oflight emitting parts “ch1” through “ch4” (in this embodiment, the numberof the light emitting parts in the light source device is equal to 4),and these light emitting parts are arrayed along a line at equaldistances. The semiconductor laser array 1 may be configured so that thelight emitting parts “ch1” through “ch4” are arrayed at equal distancesalong a slanted line that is inclined at an angle φ (φ>0) to thesub-scanning direction. Hereinafter, this angle φ will be called theinclination angle φ.

FIG. 2 shows a sub-scanning-direction imaging pattern of the laser beamfrom one of the light emitting parts of the semiconductor laser array 1to the scanned surface of the photosensitive belt 9.

In FIG. 2, the sub-scanning direction is parallel to the rotation axisof the rotary polygonal mirror 5, and the main scanning direction isperpendicular to the plane of FIG. 2.

In the imaging pattern of the laser beam shown in FIG. 2, the divergentlaser beam is emitted by one of the light emitting parts “ch1” through“ch4” of the semiconductor laser array 1. The coupling lens 2 couplesthe laser beam emitted by the semiconductor laser array 1. The aperturestop 3 restricts the diameter of the incident laser beam to theappropriate level and introduces the laser beam into the focusing lens4.

With the refraction power of the focusing lens 4, the laser beam fromthe aperture stop 4 forms a line image at the position adjacent to therotary polygonal mirror 5, the line image being elongated in the mainscanning direction. In the imaging pattern of FIG. 2, the line imageformed by the focusing lens 4 is shown as a point on the reflectionsurface of the rotary polygonal mirror 5.

The reflection surface of the rotary polygonal mirror 5 deflects thelaser beam from the focusing lens 4 while the rotary polygonal mirror 5is rotated at a constant speed around its rotation axis in the rotatingdirection (indicated by the arrow in FIG. 1).

The deflected laser beam from the rotary polygonal mirror 5 is passedthrough the focusing optical system (which is indicated by referencenumeral 6A in FIG. 2) that includes the fθ lens 6 and the elongatedfocusing lens 7, and the laser beam from the focusing optical system 6Ais reflected to the surface of the photosensitive belt 9 by thereflector mirror 8.

With the focusing action of the focusing optical system 6A, the laserbeam from the focusing optical system 6A forms a beam spot on thesurface of the photosensitive belt 9, the beam spot having a diameter ωzin the sub-scanning direction.

In the imaging pattern of FIG. 2, suppose that the aperture stop 3,which restricts the diameter of the laser beam from the coupling lens 2,is configured to have a source-side numerical aperture “NAzS” withrespect to the sub-scanning direction and the focusing optical system6A, facing the scanned surface of the photosensitive belt 9, isconfigured to have an image-side numerical aperture “NAzI” with respectto the sub-scanning direction.

The multi-beam scanning device of the present embodiment is configuredsuch that the beam spot diameter ωz in the sub-scanning direction isrepresented by the following formula:

ωz=0.82λ/NAzI  (1)

where λ is a wavelength of the laser beam emitted by the semiconductorlaser array 1, and NAzI is a numerical aperture of the focusing opticalsystem 6A with respect to the sub-scanning direction.

FIG. 3A, FIG. 3B, FIG. 3C and FIG. 3D are diagrams for explaining arelationship between the semiconductor laser array 1, the aperture stop3 and the far-field pattern.

FIG. 3A shows a configuration of the semiconductor laser array 1 of thepresent embodiment. As shown in FIG. 3A, the semiconductor laser array 1is configured such that the light emitting parts (which correspond tothe light emitting parts “ch1” through “ch4” in FIG. 1) are arrayedalong a slanted line that is at an inclination angle φ to thesub-scanning direction of the laser beam incident to the scanned surfaceof the photosensitive medium.

The inclination angle λ is measured in degrees and meets the conditions0≦φ<90.

As shown in FIG. 3A, in the present embodiment, a sub-scanning-directionarray pitch of the light emitting parts in the semiconductor laser array1, measured along the vertical line parallel to the sub-scanningdirection, is represented by “ρ·cos φ” where ρ is an array pitch of thelight emitting parts of the laser array 1 along the slanted line and φis the inclination angle of the light emitting parts of thesemiconductor laser array 1.

In the present embodiment, a scanning line pitch P, which is a distancebetween the main scanning lines on the scanned surface of thephotosensitive medium 9, is determined by an optical writing density(measured in “dpi”, or dots per inch) of the multi-beam scanning device.Suppose that the optical systems between the laser array 1 and thescanned surface of the photosensitive medium 9 have a composite focusingfactor βz in the sub-scanning direction.

In the multi-beam scanning device of the present embodiment, it isnecessary to meet the following equation:

βz=P/(ρ·cos φ)  (2)

Suppose that the aperture stop 3 has the source-side numerical apertureNAzS with respect to the sub-scanning direction and the focusing opticalsystem 6A has the image-side numerical aperture NAzI with respect to thesub-scanning direction, as shown in FIG. 2. The multi-beam scanningdevice of the present embodiment meets the following equation:

NAzS=βz NAzI  (3)

Substituting the equations (1) and (2) into the equation (3) yields thefollowing equation:

NAzS={P/(ρ·cos φ)}{0.82λ/ωz}  (4)

Suppose that a parameter K is defined by the equation:

K=0.82λ/ωz,

where λ is a wavelength of the emitted laser beams and ωz is a targetbeam spot diameter in the sub-scanning direction. The above equation (4)is rewritten into the following equation:

NAzS=K·P/(ρ·cos φ)  (4′)

As is apparent from the FIG. 2, the aperture stop 3 is configured tohave the source-side numerical aperture NAzS with respect to thesub-scanning direction.

If the numerical aperture NAzS of the aperture stop 3 is not properlyset, the multi-beam scanning device will have the following problems.When the aperture stop 3 is configured to have a too small numericalaperture NAzS, the multi-beam scanning device is difficult to perform ahigh-speed optical scanning due to insufficient light energy. On theother hand, when the aperture stop 3 is configured to have a too largenumerical aperture NAzS, the multi-beam scanning device is liable tovariations of the divergence angle for each of the respective beam spotson the scanned surface.

In the multi-beam scanning device of the present embodiment, the valueof the parameter

K(=0.82λ/ωz)

is determined by the wavelength λ of the emitted laser beams and thetarget beam spot diameter ωz in the sub-scanning direction. The value ofthe parameter K is related to the above-described depth clearance in thesub-scanning direction.

Suppose that the wavelength λ ranges from 400 nm to 800 nm and thetarget beam spot diameter ωz ranges from 16 μm to 160 μm. The followingtable is the results of calculations of the parameter K and the depthclearance W corresponding to such values of the wavelength λ and thetarget beam spot diameter ωz.

λ (nm) ωz (μm) K W (mm) 800 22 0.0298 0.90 800 50 0.0131 4.65 800 600.0109 6.69 780 22 0.0291 0.92 780 30 0.0213 1.72 780 50 0.0128 4.77 40016 0.0205 0.95 400 30 0.0109 3.35

It is known from practical experience that the depth clearance W that isabove 0.9 mm is needed to eliminate the component part errors or theassembly errors. Accordingly, as long as the supposition that thewavelength λ ranges from 400 nm to 800 nm and the target beam spotdiameter ωz ranges from 16 μm to 160 μm is made, the multi-beam scanningdevice of the present embodiment is configured such that the parameter Ksatisfies the following conditions:

0.011<K<0.030  (5)

The upper limit of the source-side numerical aperture NAzS must bedetermined by taking into consideration the elimination of thevariations of the divergence angle for each of the respective beam spotson the scanned surface.

FIG. 3B, FIG. 3C and FIG. 3D respectively show the relationship betweenthe laser beam condition at the aperture stop 3 and the far-fieldpattern when the inclination angle φ is equal to 0, 45 and 90 degrees.

The divergence angle θ of the divergent laser beam emitted from thelight emitting part of the laser array 1 when the beam power is above ½of the peak value of the power distribution is larger than at least 20degrees. As shown in FIG. 3B through FIG. 3D, in a case of theinclination angle φ=0 (FIG. 3B), the divergence angle θ in thesub-scanning direction is minimum.

Accordingly, the multi-beam scanning device of the present embodiment isconfigured such that the numerical aperture NAzS of the aperture stop 3satisfies the following condition:

NAzS≦sin[tan⁻¹{{square root over ( )}[(2/In2)tan(θ/2)]}]  (6)

When the divergence angle θ is equal to 20 degrees, the above formula(6) is written into

NAzS≦0.30  (6′)

In practical applications, the multi-beam scanning device may beconfigured to satisfy the above condition (6′).

The lower limit of the source-side numerical aperture NAzS must bedetermined by taking into consideration the composite focusing factor βzof the optical systems between the laser array 1 and the scanned surface9 in the sub-scanning direction. Specifically, this composite focusingfactor βz is calculated by a product of a lateral magnification factor|β1| of the optical systems (the coupling lens 2 and the cylindricallens 4) between the laser array 1 and the rotary deflector 5 in thesub-scanning direction and a lateral magnification factor |β2| of theoptical systems (the fθ lens 6 and the elongated focusing lens 7) of thefocusing optical system 6A in the sub-scanning direction. Namely, thecomposite focusing factor βz of the optical systems between the laserarray 1 and the scanned surface 9 in the sub-scanning direction iscalculated in accordance with the equation

βz=|β1|·|β2|.

It is known from practical experience that the lower limit of |β1| isabove 1.8. Namely, |β1|≧1.8. When |β1|<1.8, the location of thecylindrical lens 4 is too close to the rotary deflector 5, and it isdifficult to install the cylindrical lens 4 and the rotary deflector 5with no interference. To avoid the interference between the cylindricallens 4 and the rotary deflector 5 and ensure an adequate lateralmagnification factor, it is necessary to enlarge the distance of thecoupling lens 2 and the laser array 1. However, if the distance isenlarged, the coupling lens 2 can couple only a very small lightquantity of the laser beams from the laser array 1 and the multi-beamscanning device is liable to insufficient light energy.

Further, it is known from practical experience that the effective rangeof the lateral magnification factor |β2| of the optical systems of thefocusing optical system 6A in the sub-scanning direction is0.5≦|β2|≦2.0. When |β2|≦0.5, installing the focusing lens 7 at aposition that is very close to the scanned surface 9 is required. Thelength of the focusing lens 7 in the main scanning direction must beincreased and the manufacturing process of such focusing lens 7 becomesexpensive. When |β2|≦2, 0, the variations of the image surface positioncaused by the assembly errors or the like are increased, which causesthe multi-beam scanning device to be difficult to perform the multi-beamscanning at a higher density above 600 dpi.

From the foregoing considerations, the lower limit of the compositefocusing factor

βz(=|β1|·|β2|)

is determined as being about 0.9(=1.8×0.5).

From the above formulas (2) and (4′), the equation

NAzS=βz·K

is obtained. As the lower limit of the parameter K is 0.011, thesource-side numerical aperture NAzS of the aperture stop 3 must satisfythe following condition:

NAzS≧0.01  (7)

From the above formulas (6′) and (7),

0.01≦NAzS≦0.30  (8)

By using the above equation (4′):

NAzS=K·P/(ρ·cos φ),

0.01<K·P/(ρ·cos φ)<0.30  (9)

Accordingly, the multi-beam scanning device of the present embodiment isconfigured such that the above conditions (9) are satisfied.

Suppose that the wavelength λ ranges from 400 nm to 800 nm and thetarget beam spot diameter ωz is set to 30 μm. The following table is theresults of calculations of the parameter K and the depth clearance Wcorresponding to such values of the wavelength λ and the target beamspot diameter ωz.

λ (nm) ωz (μm) K W (mm) 800 30 0.022 1.67 780 30 0.021 1.72 700 30 0.0191.91 600 30 0.016 2.23 550 30 0.015 2.43 500 30 0.014 2.68 450 30 0.0122.97 400 30 0.011 3.35

It is readily understood from the above table that, when the target beamspot diameter ωz is set to the same value (30 μm), the the wavelength λ,the larger the depth clearance W. When the wavelength λ is set to asmall value, the depth clearance W becomes large and the accuracyrequirements of the optical systems become easy to satisfy. Therefore,it is possible to make the multi-beam scanning device of the presentembodiment inexpensive. Further, when the wavelength λ is set to a smallvalue, the numerical aperture NAzS can be set to a small value. Hence,the multi-beam scanning device of the present embodiment is effective ineliminating the variations of the divergence angle.

From the forgoing considerations, it is preferred that the multi-beamscanning device of the present embodiment is configured such that thewavelength λ of the emitted laser beams is below 700 nm.

As described above with reference to FIG. 1 and FIG. 2, in themulti-beam scanning device of the present embodiment, the semiconductorlaser array 1 is configured such that the light emitting parts arearrayed along a line that is at the inclination angle φ to thesub-scanning direction, the inclination angle φ measured in degrees andmeeting the conditions 0≦φ<90, and that the scanning line pitch P, thearray pitch ρ of the light emitting parts of the laser array 1 and theparameter K defined by the equation

K=0.82λ/ωz,

where λ is the wavelength of the emitted laser beams and ωz is thetarget beam spot diameter in the sub-scanning direction, satisfy thefollowing conditions:

0.01<K·P/(ρ·cos φ)<0.30  (9)

0.011<K<0.030  (5)

According to the above configuration, the multi-beam scanning device andmethod of the present embodiment can achieve the depth clearance that isabove 0.9 mm. Therefore, it is possible to ensure adequate depthclearance when the optical scanning is performed at a high density. Themulti-beam scanning device and method of the present embodiment areeffective in reducing the variations of the beam spots on the scannedsurface, so that the multi-beam scanning is carried out with accuratebeam spot diameter so as to create good quality of a reproduced image.Therefore, the image forming apparatus in which the multi-beam scanningdevice of the present invention is provided can create good quality of areproduced image.

Further, in the multi-beam scanning device of the present embodimentaccording to the above configuration, the coupling lens 2 couples thelaser beams emitted by the laser array 1. The aperture stop 3 restrictsthe diameter of the laser beams passed through the coupling lens 2. Theline focusing lens 4 provides a refraction power to the laser beams,passed through the aperture stop 3, with respect to only thesub-scanning direction. The rotary deflector 5 includes the reflectionsurfaces, the rotary deflector 5 deflects the laser beams from the laserarray 1 by one of the reflection surfaces. The focusing optical system6A focuses the deflected laser beams from the rotary deflector 5 ontothe scanned surface 9 to form the beam spots thereon.

Further, the light source device of the present embodiment for use inthe multi-beam scanning device according to the above configuration,includes the semiconductor laser array 1, the coupling lens 2 and theaperture stop 3, wherein the aperture stop is configured to have anumerical aperture NAzS in the sub-scanning direction that satisfies theconditions:

0.01<NAzS<0.30  (3)

Next, a description will be given of first through sixth preferredembodiments of the multi-beam scanning device of the invention withreference to the accompanying drawings FIG. 4 through FIG. 15B.

In some of the following preferred embodiments, one or a plurality oflenses having a non-spherical configuration may be provided in thefocusing optical system 6A. First, a description will be provided of thenon-spherical configuration of such lenses. However, the presentinvention is not limited to the non-spherical configuration of suchlenses, which will be described below.

A non-circular configuration of a lens of the focusing optical system6A, which is taken along a main-scanning cross-section (which is a flatcross-sectional plane containing the optical axis and being parallel tothe main scanning direction), is expressed as follows.

Suppose that “X” indicates a depth in the optical axis direction, “Y”indicates a coordinate in the main scanning direction, “Rm” indicates aradius of a paraxial curvature within the main-scanning cross-section,and “Km” and “Ai” (i=1, 2, 3, . . . ) indicate main-scanningcoefficients. The depth X in the optical axis direction is representedby the following equation:

X=(Y ² /R _(m))/[1+{square root over ( )}{(1+K _(m))(Y/R _(m))² }]+ΣA_(i) Y ^(i)  (10)

When a curvature within a sub-scanning cross-section (is a flatcross-sectional plane perpendicular to the main scanning direction) isvaried depending on the coordinate Y within the sub-scanningcross-section in the main scanning direction, the curvature Cs(Y) isrepresented by the following equation:

C _(s)(Y)={1/R _(s)(0)}+ΣB _(i) Y ^(i)  (11)

where “R_(s)(0)” indicates a radius of a paraxial curvature within thesub-scanning cross-section at Y=0, “Bi” indicates sub-scanningcoefficients, and “i” indicates an integer (i=1, 2, 3, . . . ).

Next, the expression of a non-circular configuration of a lens of thefocusing optical system 6A will be considered for a case in which theconfiguration of the lens within the main-scanning cross-section isnon-circular, the configuration of the lens within the sub-scanningcross-section is non-circular, and the non-circular configuration of thelens within the sub-scanning cross-section is varied depending on thecoordinate “Y” in the main-scanning direction. Suppose that “Z”indicates a coordinate in the sub-scanning direction. The depth X in theoptical axis direction in this case is represented by the followingequation: $\begin{matrix}\begin{matrix}{X = \quad {{\left( {Y^{2}/R_{m}} \right)/\left\lbrack {1 + \sqrt{\left\{ {\left( {1 + K_{m}} \right)\quad \left( {Y/R_{m}} \right)^{2}} \right\}}}\quad \right\rbrack} +}} \\{\quad {{\sum{A_{i}Y^{i}}} +}} \\{\quad {{{C_{S}(Y)} \cdot {Z^{2}/\left\lbrack {1 + \sqrt{\left\{ {\left( {1 + K_{S}} \right)\quad \left( {{C_{S}(Y)} \cdot Z} \right)^{2}} \right\}}}\quad \right\rbrack}} +}} \\{\quad {{\left( {F_{0} + {F_{1} \cdot Y} + {F_{2} \cdot Y^{2}} + {F_{3} \cdot Y^{3}} + {F_{4} \cdot Y^{4}} + \ldots} \right) \cdot Z} +}} \\{\quad {{\left( {G_{0} + {G_{1} \cdot Y} + {G_{2} \cdot Y^{2}} + {G_{3} \cdot G^{3}} + {G_{4} \cdot G^{4}} + \ldots} \right) \cdot Z^{2}} +}} \\{\quad {{\left( {H_{0} + {H_{1} \cdot Y} + {H_{2} \cdot Y^{2}} + {H_{3} \cdot H^{3}} + {H_{4} \cdot Y^{4}} + \ldots} \right) \cdot Z^{3}} +}} \\{\quad {{\left( {I_{0} + {I_{1} \cdot Y} + {I_{2} \cdot Y^{2}} + {I_{3} \cdot Y^{3}} + {I_{4} \cdot Y^{4}} + \ldots} \right) \cdot Z^{4}} +}} \\{\quad {{\left( {J_{0} + {J_{1} \cdot Y} + {J_{2} \cdot Y^{2}} + {J_{3} \cdot Y^{3}} + {J_{4} \cdot Y^{4}} + \ldots} \right) \cdot Z^{5}} +}} \\{\quad {{\left( {K_{0} + {K_{1} \cdot Y} + {K_{2} \cdot Y^{2}} + {K_{3} \cdot Y^{3}} + {K_{4} \cdot Y^{4}} + \ldots} \right) \cdot Z^{6}} +}} \\{\quad {{\left( {L_{0} + {L_{1} \cdot Y} + {L_{2} \cdot Y^{2}} + {L_{3} \cdot Y^{3}} + {L_{4} \cdot Y^{4}} + \ldots} \right) \cdot Z^{7}} +}} \\{\quad {{\left( {M_{0} + {M_{1} \cdot Y} + {M_{2} \cdot Y^{2}} + {M_{3} \cdot Y^{3}} + {M_{4} \cdot Y^{4}} + \ldots} \right) \cdot Z^{8}} +}} \\{\quad {{\left( {N_{0} + {N_{1} \cdot Y} + {N_{2} \cdot Y^{2}} + {N_{3} \cdot Y^{3}} + {N_{4} \cdot Y^{4}} + \ldots} \right) \cdot Z^{9}} +}} \\{\quad \ldots}\end{matrix} & (12)\end{matrix}$

where the coefficient “Ks” included in the third term of the equation(12) is represented by the equation

Ks(Y)=Ks(0)+Ci Y ^(i)  (13)

where “Ks(0)” indicates a conical coefficient within the sub-scanningcross-section at Y=0, “Ci” indicates sub-scanning coefficients, and “i”indicates an integer (i=1, 2, 3, . . . ).

FIG. 4 shows a configuration of the optical systems of a first preferredembodiment of the multi-beam scanning device.

As shown in FIG. 4, the multi-beam scanning device of this embodimentgenerally comprises a semiconductor laser array 111, a coupling lens121, an aperture stop 131, a cylindrical lens 141, a rotary polygonalmirror 151, lenses 161, 171 and 181 of the focusing optical system, anda scanned surface 19 of the photosensitive medium.

It is a matter of course that a planer mirror may be provided at anintermediate portion of the optical path between the light source 111and the scanned surface 19 to bend the optical path in conformity withthe practical layout of the multi-beam scanning device.

In the configuration of FIG. 4, the semiconductor laser array 111 isprovided with four light emitting parts, the array pitch ρ of the lightemitting parts ρ=14 μm, the emitted laser beam wavelength 780 nm, themaximum output power 15 mW, and the inclination angle φ=0 degrees.

The coupling lens 121 is provided with a one-group, two-lensconfiguration, the focal length 30 mm, and the collimating function.

The cylindrical lens 141 is provided with the focal length 70.62 mm inthe sub-scanning direction.

The aperture stop 131 is provided with the aperture width 5.2 mm in themain scanning direction and the aperture width 1.04 mm in thesub-scanning direction.

The rotary polygonal mirror 151 is provided with six reflectionsurfaces, the inscribed circle radius 25 mm, the incident angle (betweenthe laser beam incident direction of the light source and the opticalaxis of the focusing optical system) 60 degrees, the writing density1200 dpi, and the target beam spot diameter 50 μm.

The lenses 161, 171 and 181 of the focusing optical system areconfigured as in the following table. Suppose that “Rmi” indicates theradius of curvature of the i-th surface (counted from the side of therotary polygonal mirror) within the main-scanning cross-section, “Rsi”indicates the radius of curvature of the i-th surface within thesub-scanning cross-section, “X” indicates the distance between thesurfaces, “Y” indicates the shift amount of the surface in the upwarddirection in the plane of the shown configuration, and “n” indicates therefractive index. In the case of a lens having a non-circularconfiguration, the radius “Rmi” and the radius “Rsi” indicates theradius of the paraxial curvature of the i-th surface of suchconfiguration. The notation of the following table is applied to otherpreferred embodiments which will be described later.

i Rmi Rsi X Y n Mirror Surface 0 ∞ ∞ 51.38 1.627 Lens 161 1 −96.76spherical 15.07 0 1.78571 2 −93.27 spherical 9.76 0 Lens 171 3 −2450.2spherical 19.90 0 1.60909 4 −161.76 spherical 127.0 0 Lens 181 5 −630.00−55.53 3.00 0 1.57211 6 −700.00 −24.42 101.72 0

The incident-side surface of the lens 181 (with the surface number i=5)has the main-scanning cross-section in the non-circular configuration.The non-circular configuration of this surface taken along themain-scanning cross-section is represented by the above equation (10).The following TABLE 1 provides the values of the main-scanningcoefficients of the equation (10).

TABLE 1 Surface No. Main-Scanning Coefficients 5 K  −31.405 A₄  −2.059 ×10⁻⁹  A₆   1.839 × 10⁻¹⁴ A₈   6.366 × 10⁻¹⁸ A₁₀ −8.922 × 10⁻²² A₁₂ 6.466 × 10⁻²⁶ A₁₄ −1.339 × 10⁻³⁰ A₁₆ −1.058 × 10⁻³⁴ A₁₈  4.413 × 10⁻³⁹

In the first preferred embodiment, the multi-beam scanning device isconfigured to have the parameter K which is given by

K=0.82×780×10⁻³/50=0.01279.

The configuration of this embodiment meets the conditions of the aboveformula (5). In the first preferred embodiment, the multi-beam scanningdevice is configured to have the parameter

K·P/(ρ·cos φ)

which is given by $\begin{matrix}{{K \cdot {P/\left( {{\rho \cdot \cos}\quad \varphi} \right)}} = \quad {0.01279 \times {21.167/14}}} \\{= \quad {0.01934\quad.}}\end{matrix}$

The configuration of this embodiment meets the conditions of the aboveformula (9).

FIG. 5A and FIG. 5B are diagrams for explaining the relationship betweenthe defocus amount and the spot diameter in the multi-beam scanningdevice of FIG. 4.

In the first preferred embodiment, the light emitting part “ch1” of thesemiconductor laser array is positioned 21 μm apart from the opticalaxis of the coupling lens 121 in the sub-scanning direction. Withrespect to the defocus amount of the beam spot (which is formed on thescanned surface by the laser beam emitted from the light emitting part“ch1”) at image-height positions of nine equal subdivisions of ±150 mm,the relationship between the defocus amount and the beam spot diameterin the main scanning direction is shown in FIG. 5A. Similarly, therelationship between the defocus amount and the beam spot diameter inthe sub-scanning direction is shown in FIG. 5B.

As shown in FIG. 5A, the depth clearance in the main scanning directionis 3.10 mm. As shown in FIG. 5B, the depth clearance in the sub-scanningdirection is 2.25 mm. As both the depth clearances of this embodimentare larger than 0.9 mm (based on the practical experience), themulti-beam scanning device of this embodiment ensures adequate depthclearance even when the optical scanning is performed at the writingdensity of 1200 dpi, and effectively reduces the variations of the beamspots on the scanned surface to the small level so that the multi-beamscanning is carried out with accurate beam spot diameter.

The numerical aperture NAzS of this embodiment is 0.01934. It isconfirmed that the variations of the divergence angle for the respectivelight emitting parts of the semiconductor laser array are effectivelyreduced. When a photoconductive material having the exposure energy of4.4 mJ/m² is used as the photosensitive medium in this embodiment, thethreshold level of the exposure energy at the scanning speed 380.8 m/secis 11.44 mW. As the maximum output power of the laser array in thisembodiment is 15 mW, the insufficient light energy as in theconventional multi-beam scanning device does not occur for the presentembodiment.

Next, FIG. 6 shows a configuration of the optical systems of a secondpreferred embodiment of the multi-beam scanning device.

As shown in FIG. 6, the multi-beam scanning device of this embodimentgenerally comprises a semiconductor laser array 112, a coupling lens122, an aperture stop 132, a cylindrical lens 142, a rotary polygonalmirror 152, lenses 162 and 172 of the focusing optical system, and thescanned surface 19 of the photosensitive medium.

It is a matter of course that a planer mirror may be provided at anintermediate portion of the optical path between the light source 112and the scanned surface 19 to bend the optical path in conformity withthe practical layout of the multi-beam scanning device.

In the configuration of FIG. 6, the semiconductor laser array 112 isprovided with four light emitting parts, the array pitch ρ of the lightemitting parts ρ=20 μm, the emitted laser beam wavelength 670 nm, themaximum output power 8 mW, and the inclination angle φ=29.45 degrees.

The coupling lens 122 is provided with a single lens configuration, thefocal length 30 mm, and the collimating function.

The cylindrical lens 142 is provided with the focal length 51.88 mm inthe sub-scanning direction.

The aperture stop 132 is provided with the aperture width 7.9 mm in themain scanning direction and the aperture width 1.2 mm in thesub-scanning direction.

The rotary polygonal mirror 152 is provided with five reflectionsurfaces, the inscribed circle radius 18 mm, the incident angle (betweenthe laser beam incident direction of the light source and the opticalaxis of the focusing optical system) 60 degrees, the writing density1200 dpi, and the target beam spot diameter 30 μm.

The lenses 162 and 172 of the focusing optical system are configured asin the following table.

i Rmi Rsi X Y n Mirror Surface 0 ∞ ∞ 72.49 0.206 Lens 162 1 1617.54−52.00 35.00 0 1.52657 2 −146.53 −195.27 62.91 0.204 Lens 172 3 413.68−71.31 13.94 0 1.52657 4 824.88 −27.70 160.22 0

The surfaces (the surface number i=1, 2, 3) of the lenses 162 and 172have the non-circular configuration represented by the above equations(10) and (11). The surface (the surface number i=4) of the lens 172 hasthe non-circular configuration represented by the above equations (11)through (13). The following TABLE 2 through TABLE 6 provide the valuesof the main-scanning coefficients and the sub-scanning coefficients ofthe equations (10) through (13)).

TABLE 2 Surface Main-Scanning Sub-Scanning Number CoefficientsCoefficients 1 K  185  B₁ −1.069 × 10⁻⁵  A₁ 0 B₂ 2.323 × 10⁻⁶ A₂ 0 B₃2.768 × 10⁻⁹ A₃ 0 B₄ −2.010 × 10⁻¹⁰ A₄ 1.284 × 10⁻⁸ B₅ −5.286 × 10⁻¹³ A₅0 B₆  1.603 × 10⁻¹⁴ A₆ −6.017 × 10⁻¹³ B₇  4.005 × 10⁻¹⁷ A₇ 0 B₈ −5.616 ×10⁻¹⁹ A₈ −8.040 × 10⁻¹⁷ B₉  1.444 × 10⁻²⁰ A₉ 0  B₁₀ −1.834 × 10⁻²¹  A₁₀ 5.138 × 10⁻²¹  B₁₁ −2.465 × 10⁻²⁴  A₁₁ 0  B₁₂  1.419 × 10⁻²⁵

TABLE 3 Surface Main-Scanning Sub-Scanning Number CoefficientsCoefficients 2 K  −1.934 × 10⁻¹  B₁ 0 A₁ 0 B₂ −2.116 × 10⁻⁶  A₂ 0 B₃ 0A₃ 0 B₄  4.472 × 10⁻¹¹ A₄ 1.790 × 10⁻⁸ B₅ 0 A₅ 0 B₆  3.322 × 10⁻¹⁴ A₆ 2.847 × 10⁻¹³ B₇ 0 A₇ 0 B₈ −1.366 × 10⁻¹⁸ A₈ −3.723 × 10⁻¹⁷ B₉ 0 A₉ 0 B₁₀ −6.548 × 10⁻²²  A₁₀  5.930 × 10⁻²¹  B₁₁ 0  A₁₁ 0  B₁₂ −4.619 ×10⁻²⁶

TABLE 4 Surface Main-Scanning Sub-Scanning Number CoefficientsCoefficients 3 K  −13.95 B₁ 0 A₁ 0 B₂ −1.958 × 10⁻⁷  A₂ 0 B₃ 0 A₃ 0 B₄ 2.316 × 10⁻¹¹ A₄ −6.790 × 10⁻⁹  B₅ 0 A₅ 0 B₆ −1.140 × 10⁻¹⁵ A₆ −2.046 ×10⁻¹³ B₇ 0 A₇ 0 B₈  1.179 × 10⁻²⁰ A₈  7.466 × 10⁻¹⁸ B₉ 0 A₉ 0  B₁₀ 9.187 × 10⁻²⁵  A₁₀  5.282 × 10⁻²²  B₁₁ 0  A₁₁ 0  B₁₂ −5.552 × 10⁻²⁹ A₁₂ −8.143 × 10⁻²⁷  B₁₃ 0  A₁₃ 0  B₁₄ 0  A₁₄ −3.771 × 10⁻³³  B₁₅ 0

TABLE 5 Surface Main-Scanning Sub-Scanning Number CoefficientsCoefficients 4 K  −69.07 B₁ −9.030 × 10⁻⁷  A₁ 0 B₂ 4.204 × 10⁻⁷ A₂ 0 B₃−2.211 × 10⁻¹¹ A₃ 0 B₄ −3.115 × 10⁻¹¹ A₄ −1.348 × 10⁻⁸ B₅  1.857 × 10⁻¹⁵A₅ 0 B₆  1.289 × 10⁻¹⁵ A₆  8.953 × 10⁻¹⁴ B₇ −1.444 × 10⁻¹⁹ A₇ 0 B₈ 3.211 × 10⁻²¹ A₈  1.936 × 10⁻¹⁷ B₉  2.173 × 10⁻²³ A₉ 0  B₁₀ −9.827 ×10⁻²⁵  A₁₀ −2.840 × 10⁻²²  B₁₁ −9.598 × 10⁻²⁸  A₁₁ 0  B₁₂ −1.663 × 10⁻²⁹ A₁₂  6.044 × 10⁻²⁷  B₁₃ 0  A₁₃ 0  B₁₄ 0  A₁₄  1.077 × 10⁻³¹  B₁₅ 0

TABLE 6 4 C₀ −1.000 I₀ −8.009 × 10⁻⁷  K₀ −1.179 × 10⁻⁹  C₁ 0 I₁ −8.846 ×10⁻¹¹ K₁ −9.850 × 10⁻¹³ C₂ 0 I₂  7.158 × 10⁻¹¹ K₂ −9.672 × 10⁻¹⁴ C₃ 0 I₃−1.870 × 10⁻¹³ K₃  1.828 × 10⁻¹⁵ C₄ 0 I₄ −2.617 × 10⁻¹⁴ K₄  1.860 ×10⁻¹⁶ C₅ 0 I₅  6.722 × 10⁻¹⁷ K₅ −6.285 × 10⁻¹⁹ C₆ 0 I₆  5.872 × 10⁻¹⁸ K₆−5.428 × 10⁻²⁰ C₇ 0 I₇ −9.322 × 10⁻²¹ K₇  8.632 × 10⁻²³ C₈ 0 I₈ −6.141 ×10⁻²² K₈  6.187 × 10⁻²⁴ C₉ 0 I₉  5.471 × 10⁻²⁵ K₉ −5.030 × 10⁻²⁷  C₁₀ 0 I₁₀  2.868 × 10⁻²⁶  K₁₀ −3.015 × 10⁻²⁸  C₁₁ 0  I₁₁ −1.116 × 10⁻²⁹  K₁₁ 1.019 × 10⁻³¹  C₁₂ 0  I₁₂ −4.938 × 10⁻³¹  K₁₂  5.340 × 10⁻³³

In the second preferred embodiment, the multi-beam scanning device isconfigured to have the parameter K which is given by

K=0.82×670×10⁻³/30=0.01831.

The configuration of this embodiment meets the conditions of the aboveformula (5). In the second preferred embodiment, the multi-beam scanningdevice is configured to have the parameter

K·P/(ρ·cos φ)

which is given by $\begin{matrix}{{K \cdot {P/\left( {{\rho \cdot \cos}\quad \varphi} \right)}} = \quad {0.01831 \times {{21.167/20} \cdot \cos}\quad \left( {29.45\quad {\deg.}} \right)}} \\{= \quad {0.02225\quad.}}\end{matrix}$

The configuration of this embodiment meets the conditions of the aboveformula (9).

FIG. 7A and FIG. 7B are diagrams for explaining the relationship betweenthe defocus amount and the spot diameter in the multi-beam scanningdevice of FIG. 6.

In the second preferred embodiment, the light emitting part “ch1” of thesemiconductor laser array is positioned 28.43 μm apart from the opticalaxis of the coupling lens 122 in the sub-scanning direction. Withrespect to the defocus amount of the beam spot (which is formed on thescanned surface by the laser beam emitted from the light emitting part“ch1” ) at image-height positions of twenty-one equal subdivisions of±150 mm, the relationship between the defocus amount and the beam spotdiameter in the main scanning direction is shown in FIG. 7A. Similarly,the relationship between the defocus amount and the beam spot diameterin the sub-scanning direction is shown in FIG. 7B.

As shown in FIG. 7A, the depth clearance in the main scanning directionis 1.57 mm. As shown in FIG. 7B, the depth clearance in the sub-scanningdirection is 2.00 mm. As both the depth clearances of this embodimentare larger than 0.9 mm (based on the practical experience), themulti-beam scanning device of this embodiment ensures adequate depthclearance even when the optical scanning is performed at the writingdensity of 1200 dpi, and effectively reduces the variations of the beamspots on the scanned surface to the small level so that the multi-beamscanning is carried out with accurate beam spot diameter.

The numerical aperture NAzS of this embodiment is 0.02225. It isconfirmed that the variations of the divergence angle for the respectivelight emitting parts of the semiconductor laser array are effectivelyreduced. When a photoconductive material having the exposure energy of6.3 mJ/m² is used as the photosensitive medium in this embodiment, thethreshold level of the exposure energy at the scanning speed 380.8 m/secis 7.22 mW. As the maximum output power of the laser array in thisembodiment is 8 mW, the insufficient light energy as in the conventionalmulti-beam scanning device does not occur for the present embodiment.

Next, FIG. 8 shows a configuration of the optical systems of a thirdpreferred embodiment of the multi-beam scanning device.

As shown in FIG. 8, the multi-beam scanning device of this embodimentgenerally comprises a semiconductor laser array 113, a coupling lens123, an aperture stop 133, a cylindrical lens 143, a rotary polygonalmirror 153, lenses 163, 173 and 183 of the focusing optical system, andthe scanned surface 19 of the photosensitive medium.

It is a matter of course that a planer mirror may be provided at anintermediate portion of the optical path between the light source 113and the scanned surface 19 to bend the optical path in conformity withthe practical layout of the multi-beam scanning device.

In the configuration of FIG. 8, the semiconductor laser array 113 isprovided with four light emitting parts, the array pitch ρ of the lightemitting parts ρ=14 μm, the emitted laser beam wavelength 780 nm, themaximum output power 10 mW, and the inclination angle φ=0 degrees.

The coupling lens 123 is provided with a single lens configuration, thefocal length 15 mm, and the collimating function.

The cylindrical lens 143 is provided with the focal length 70.62 mm inthe sub-scanning direction.

The aperture stop 133 is provided with the aperture width 5.5 mm in themain scanning direction and the aperture width 0.88 mm in thesub-scanning direction.

The rotary polygonal mirror 153 is provided with six reflectionsurfaces, the inscribed circle radius 25 mm, the incident angle (betweenthe laser beam incident direction of the light source and the opticalaxis of the focusing optical system) 60 degrees, the writing density 600dpi, and the target beam spot diameter 60 μm.

The lenses 163, 173 and 183 of the focusing optical system areconfigured as in the following table.

i Rmi Rsi X Y n Mirror Surface 0 ∞ ∞ 51.38 1.627 Lens 163 1 −96.76spherical 15.07 0 1.78571 2 −93.27 spherical 9.76 0 Lens 173 3 −2450.2spherical 19.90 0 1.60909 4 −161.76 spherical 127.0 0 Lens 183 5 −630.00−55.53 3.00 0 1.57211 6 −700.00 −24.42 101.72 0

The incident-side surface of the lens 183 (with the surface number i=5)has the main-scanning cross-section in the non-circular configuration.The non-circular configuration of this surface taken along themain-scanning cross-section is represented by the above equation (10).The following TABLE 7 provides the values of the main-scanningcoefficients of the equation (10).

TABLE 7 Surface No. Main-Scanning Coefficients 5 K −31.405 A₄  −2.059 ×10⁻⁹  A₆   1.839 × 10⁻¹⁴ A₈   6.366 × 10⁻¹⁸ A₁₀ −8.922 × 10⁻²² A₁₂ 6.466 × 10⁻²⁶ A₁₄ −1.339 × 10⁻³⁰ A₁₆ −1.058 × 10⁻³⁴ A₁₈  4.413 × 10⁻³⁹

The focusing optical system of the third preferred embodiment is thesame as that of the first preferred embodiment. In the third preferredembodiment, the multi-beam scanning device is configured to have theparameter K which is given by

K=0.82×780×10⁻³/60=0.01066.

The configuration of this embodiment meets the conditions of the aboveformula (5). In the third preferred embodiment, the multi-beam scanningdevice is configured to have the parameter

K·P/(ρ·cos φ)

which is given by $\begin{matrix}{{K \cdot {P/\left( {{\rho \cdot \cos}\quad \varphi} \right)}} = \quad {0.01066 \times {42.333/14}}} \\{= \quad {0.03223\quad.}}\end{matrix}$

The configuration of this embodiment meets the conditions of the aboveformula (9).

FIG. 9A and FIG. 9B are diagrams for explaining the relationship betweenthe defocus amount and the spot diameter in the multi-beam scanningdevice of FIG. 8.

In the third preferred embodiment, the light emitting part “ch1” of thesemiconductor laser array is positioned 21 μm apart from the opticalaxis of the coupling lens 123 in the sub-scanning direction. Withrespect to the defocus amount of the beam spot (which is formed on thescanned surface by the laser beam emitted from the light emitting part“ch1”) at image-height positions of nine equal subdivisions of ±150 mm,the relationship between the defocus amount and the beam spot diameterin the main scanning direction is shown in FIG. 9A. Similarly, therelationship between the defocus amount and the beam spot diameter inthe sub-scanning direction is shown in FIG. 9B.

As shown in FIG. 9A, the depth clearance in the main scanning directionis 8.10 mm. As shown in FIG. 9B, the depth clearance in the sub-scanningdirection is 4.51 mm. As both the depth clearances of this embodimentare larger than 0.9 mm (based on the practical experience), themulti-beam scanning device of this embodiment ensures adequate depthclearance even when the optical scanning is performed at the writingdensity of 600 dpi, and effectively reduces the variations of the beamspots on the scanned surface to the small level so that the multi-beamscanning is carried out with accurate beam spot diameter.

The numerical aperture NAzS of this embodiment is 0.03223. It isconfirmed that the variations of the divergence angle for the respectivelight emitting parts of the semiconductor laser array are effectivelyreduced. When a photoconductive material having the exposure energy of6.3 mJ/m² is used as the photosensitive medium in this embodiment, thethreshold level of the exposure energy at the scanning speed 380.8 m/secis 7.28 mW. As the maximum output power of the laser array in thisembodiment is 10 mW, the insufficient light energy as in theconventional multi-beam scanning device does not occur for the presentembodiment.

Next, FIG. 10 shows a configuration of the optical systems of a fourthpreferred embodiment of the multi-beam scanning device.

As shown in FIG. 10, the multi-beam scanning device of this embodimentgenerally comprises a semiconductor laser array 114, a coupling lens124, an aperture stop 134, a cylindrical lens 144, a rotary polygonalmirror 154, lenses 164 and 174 of the focusing optical system, and thescanned surface 19 of the photosensitive medium.

It is a matter of course that a planer mirror may be provided at anintermediate portion of the optical path between the light source 114and the scanned surface 19 to bend the optical path in conformity withthe practical layout of the multi-beam scanning device.

In the configuration of FIG. 10, the semiconductor laser array 114 isprovided with four light emitting parts, the array pitch ρ of the lightemitting parts ρ=14 μm, the emitted laser beam wavelength 780 nm, themaximum output power 10 mW, and the inclination angle φ=62.3 degrees.

The coupling lens 124 is provided with a single lens configuration, thefocal length 27 mm, and the collimating function.

The cylindrical lens 144 is provided with the focal length 126.18 mm inthe sub-scanning direction.

The aperture stop 134 is provided with the aperture width 6.56 mm in themain scanning direction and the aperture width 2.3 mm in thesub-scanning direction.

The rotary polygonal mirror 154 is provided with five reflectionsurfaces, the inscribed circle radius 18 mm, the incident angle (betweenthe laser beam incident direction of the light source and the opticalaxis of the focusing optical system) 60 degrees, the writing density1200 dpi, and the target beam spot diameter 45 μm.

The lenses 164 and 174 of the focusing optical system are configured asin the following table.

i Rmi Rsi X Y n Mirror Surface 0 ∞ ∞ 72.56 0.286 Lens 164 1 1616.43−50.14 35.00 0 1.52398 2 −146.51 −199.81 61.93 0.254 Lens 174 3 400.87−72.03 14.00 0 1.52398 4 824.88 −27.59 160.56 0

The surfaces (the surface number i=1, 2, 3) of the lenses 164 and 174have the non-circular configuration represented by the above equations(10) and (11). The surface (the surface number i=4) of the lens 174 hasthe non-circular configuration represented by the above equations (11)through (13). The following TABLE 8 through TABLE 12 provide the valuesof the main-scanning coefficients and the sub-scanning coefficients ofthe equations (10) through (13).

TABLE 8 Surface Main-Scanning Sub-Scanning Number CoefficientsCoefficients 1 K 1.976 × 10⁺² B₁ −1.162 × 10⁻⁵  A₁ 0 B₂ 2.276 × 10⁻⁶ A₂0 B₃ 2.714 × 10⁻⁹ A₃ 0 B₄ −1.544 × 10⁻¹⁰ A₄ 1.281 × 10⁻⁸ B₅ −4.265 ×10⁻¹³ A₅ 0 B₆  6.417 × 10⁻¹⁵ A₆ −6.374 × 10⁻¹³ B₇  9.179 × 10⁻¹⁹ A₇ 0 B₈−1.230 × 10⁻¹⁹ A₈ −9.428 × 10⁻¹⁷ B₉  1.453 × 10⁻²⁰ A₉ 0  B₁₀ −1.881 ×10⁻²²  A₁₀  5.965 × 10⁻²¹  B₁₁ −1.468 × 10⁻²⁴  A₁₁ 0  B₁₂ −2.670 × 10⁻²⁶

TABLE 9 Surface Main-Scanning Sub-Scanning Number CoefficientsCoefficients 2 K −1.857 × 10⁻¹  B₁ 0 A₁ 0 B₂ −2.125 × 10⁻⁶  A₂ 0 B₃ 0 A₃0 B₄ 1.805 × 10⁻¹¹ A₄ 1.774 × 10⁻⁸  B₅ 0 A₅ 0 B₈ 2.716 × 10⁻¹⁴ A₆ 1.384× 10⁻¹³ B₇ 0 A₇ 0 B₈ 6.924 × 10⁻¹⁹ A₈ −4.354 × 10⁻¹⁷  B₉ 0 A₉ 0  B₁₀−2.685 × 10⁻²²   A₁₀ 7.168 × 10⁻²¹  B₁₁ 0  A₁₁ 0  B₁₂ −5.778 × 10⁻²⁶ 

TABLE 10 Surface Main-Scanning Sub-Scanning Number CoefficientsCoefficients 3 K −12.60 B₁ 0 A₁ 0 B₂ −1.962 × 10⁻⁷  A₂ 0 B₃ 0 A₃ 0 B₄2.230 × 10⁻¹¹ A₄ −7.349 × 10⁻⁹  B₅ 0 A₅ 0 B₆ −1.022 × 10⁻¹⁵  A₆ −2.106 ×10⁻¹³ B₇ 0 A₇ 0 B₈ 1.081 × 10⁻²⁰ A₈  8.173 × 10⁻¹⁸ B₉ 0 A₉ 0  B₁₀ 6.363× 10⁻²⁵  A₁₀  5.409 × 10⁻²²  B₁₁ 0  A₁₁ 0  B₁₂ −3.645 × 10⁻²⁹   A₁₂−1.082 × 10⁻²⁶  B₁₃ 0  A₁₃ 0  B₁₄ 0  A₁₄ −2.039 × 10⁻³²  B₁₅ 0

TABLE 11 Surface Main-Scanning Sub-Scanning Number CoefficientsCoefficients 4 K −71.068 B₁ −8.546 × 10⁻⁷  A₁ 0 B₂ 4.161 × 10⁻⁷ A₂ 0 B₃−2.523 × 10⁻¹¹ A₃ 0 B₄ −2.960 × 10⁻¹¹ A₄ −1.324 × 10⁻⁸  B₅  2.114 ×10⁻¹⁶ A₅ 0 B₆  1.160 × 10⁻¹⁵ A₆ 9.662 × 10⁻¹⁴ B₇  4.372 × 10⁻²² A₇ 0 B₈−1.098 × 10⁻²¹ A₈ 1.888 × 10⁻¹⁷ B₉  5.560 × 10⁻²⁴ A₉ 0  B₁₀ −7.785 ×10⁻²⁵  A₁₀ −3.102 × 10⁻²²   B₁₁ −1.617 × 10⁻²⁹  A₁₁ 0  B₁₂  3.262 ×10⁻³⁰  A₁₂ 7.298 × 10⁻²⁷  B₁₃ 0  A₁₃ 0  B₁₄ 0  A₁₄ 2.305 × 10⁻³²  B₁₅ 0

TABLE 12 4 C₀ −3.940 ×  I₀ 2.869 × K₀ −1.526 × 10⁻¹  10⁻⁶  10⁻⁹  C₁1.796 × I₁ 4.012 × K₁ −3.101 × 10⁻⁴  10⁻¹¹ 10⁻¹¹ C₂ 2.425 × I₂ 1.690 ×K₂ −8.903 × 10⁻⁶  10⁻¹¹ 10⁻¹² C₃ 4.438 × I₃ 3.572 × K₃  5.017 × 10⁻⁸ 10⁻¹⁴ 10⁻¹⁴ C₄ 4.584 × I₄ −8.742 ×  K₄  3.241 × 10⁻¹⁰ 10⁻¹⁵ 10⁻¹⁵ C₅−2.438 ×  I₅ 1.964 × K₅ −7.703 × 10⁻¹² 10⁻¹⁸ 10⁻¹⁸ C₆ −3.396 ×  I₆ 8.603× K₆ −4.104 × 10⁻¹⁴ 10⁻¹⁹ 10⁻¹⁹ C₇ 4.132 × I₇ 6.160 × K₇  5.118 × 10⁻¹⁷10⁻²³ 10⁻²² C₈ 6.805 × I₈ −3.347 ×  K₈  2.368 × 10⁻¹⁹ 10⁻²³ 10⁻²³ C₉ 0I₉ −3.693 ×  K₉ −1.550 × 10⁻²⁸ 10⁻²⁶  C₁₀ 0  I₁₀ 4.536 ×  K₁₀ −6.371 ×10⁻²⁸ 10⁻²⁸  C₁₁ 0  I₁₁ 0  K₁₁  1.748 × 10⁻³¹  C₁₂ 0  I₁₂ 0  K₁₂  6.503× 10⁻³³

In the fourth preferred embodiment, the multi-beam scanning device isconfigured to have the parameter K which is given by

K=0.82×780×10⁻³/45=0.01421.

The configuration of this embodiment meets the conditions of the aboveformula (5). In the fourth preferred embodiment, the multi-beam scanningdevice is configured to have the parameter

K·P/(ρ·cos φ)

which is given by $\begin{matrix}{{K \cdot {P/\left( {{\rho \cdot \cos}\quad \varphi} \right)}} = \quad {0.01421 \times {{21.167/14} \cdot \cos}\quad \left( {62.3\quad {\deg.}} \right)}} \\{= \quad {0.04622\quad.}}\end{matrix}$

The configuration of this embodiment meets the conditions of the aboveformula (9).

FIG. 11A and FIG. 11B are diagrams for explaining the relationshipbetween the defocus amount and the spot diameter in the multi-beamscanning device of FIG. 10.

In the fourth preferred embodiment, the light emitting part “ch1” of thesemiconductor laser array is positioned 18.48 μm apart from the opticalaxis of the coupling lens 124 in the sub-scanning direction. Withrespect to the defocus amount of the beam spot (which is formed on thescanned surface by the laser beam emitted from the light emitting part“ch1”) at image-height positions of nine equal subdivisions of ±150 mm,the relationship between the defocus amount and the beam spot diameterin the main scanning direction is shown in FIG. 11A. Similarly, therelationship between the defocus amount and the beam spot diameter inthe sub-scanning direction is shown in FIG. 11B.

As shown in FIG. 11A, the depth clearance in the main scanning directionis 3.04 mm. As shown in FIG. 11B, the depth clearance in thesub-scanning direction is 3.93 mm. As both the depth clearances of thisembodiment are larger than 0.9 mm (based on the practical experience),the multi-beam scanning device of this embodiment ensures adequate depthclearance even when the optical scanning is performed at the writingdensity of 1200 dpi, and effectively reduces the variations of the beamspots on the scanned surface to the small level so that the multi-beamscanning is carried out with accurate beam spot diameter.

The numerical aperture NAzS of this embodiment is 0.04622. It isconfirmed that the variations of the divergence angle for the respectivelight emitting parts of the semiconductor laser array are effectivelyreduced. When a photoconductive material having the exposure energy of6.3 mJ/m² is used as the photosensitive medium in this embodiment, thethreshold level of the exposure energy at the scanning speed 380.8 m/secis 7.40 mW. As the maximum output power of the laser array in thisembodiment is 10 mW, the insufficient light energy as in theconventional multi-beam scanning device does not occur for the presentembodiment.

Next, FIG. 12A and FIG. 12B show a configuration of the optical systemsof a fifth preferred embodiment of the multi-beam scanning device. Theconfiguration of this embodiment in the main scanning direction is shownin FIG. 12A, and the configuration of this embodiment in thesub-scanning direction is shown in FIG. 12B.

As shown in FIG. 12A and FIG. 12B, the multi-beam scanning device ofthis embodiment generally comprises a semiconductor laser array 115, acoupling lens 125, an aperture stop 135, a cylindrical lens 145, arotary polygonal mirror 155, three lenses 165, 175 and 185 and acylindrical mirror 18M of the focusing optical system, and the scannedsurface 19 of the photosensitive medium.

It is a matter of course that a planer mirror may be provided at anintermediate portion of the optical path between the light source 115and the scanned surface 19 to bend the optical path in conformity withthe practical layout of the multi-beam scanning device.

In the configuration of FIG. 12A and FIG. 12B, the semiconductor laserarray 115 is provided with four light emitting parts, the array pitch ρof the light emitting parts ρ=10 μm, the emitted laser beam wavelength670 nm, the maximum output power 8 mW, and the inclination angle φ=0degrees.

The coupling lens 125 is provided with a two-group, three-lensconfiguration, the focal length 22 mm, and the collimating function.

The cylindrical lens 145 is provided with a two-lens combinedconfiguration and the focal length 189.77 mm in the sub-scanningdirection.

The aperture stop 135 is provided with the aperture width 10.5 mm in themain scanning direction and the aperture width 1.96 mm in thesub-scanning direction.

The rotary polygonal mirror 156 is provided with six reflectionsurfaces, the inscribed circle radius 65 mm, the incident angle 60degrees, the writing density 850 dpi, and the target beam spot diameter35 μm.

The lenses 165, 175, 185 and the mirror 18M of the focusing opticalsystem are configured as in the following table.

i Rmi Rsi X Y n Mirror Surface 0 ∞ ∞ 45.50 0.499 Lens 165 1 −78.22spherical 9.80 0 1.58700 2 −1115.4 spherical 3.95 0 Lens 175 3 −318.06spherical 20.6 0 1.78097 4 −112.85 spherical 2.04 0 Lens 185 5 639.11spherical 23.00 0 1.45419 6 −158.15 spherical 315.00 0 Mirror 18M 7 ∞−169.87 99.97 0

In the fifth preferred embodiment, the multi-beam scanning device isconfigured to have the parameter K which is given by

K=0.82×670×10⁻³/35=0.01570.

The configuration of this embodiment meets the conditions of the aboveformula (5). In the third preferred embodiment, the multi-beam scanningdevice is configured to have the parameter

K·P/(ρ·cos φ)

which is given by $\begin{matrix}{{K \cdot {P/\left( {{\rho \cdot \cos}\quad \varphi} \right)}} = \quad {0.0570 \times {29.882/10}}} \\{= \quad {0.04691\quad.}}\end{matrix}$

The configuration of this embodiment meets the conditions of the aboveformula (9).

FIG. 13A and FIG. 13B are diagrams for explaining the relationshipbetween the defocus amount and the spot diameter in the multi-beamscanning device of FIG. 12A and FIG. 12B.

In the fifth preferred embodiment, the light emitting part “ch1” of thesemiconductor laser array is positioned 15 μm apart from the opticalaxis of the coupling lens 125 in the sub-scanning direction. Withrespect to the defocus amount of the beam spot (which is formed on thescanned surface by the laser beam emitted from the light emitting part“ch1”) at image-height positions of nine equal subdivisions of ±150 mm,the relationship between the defocus amount and the beam spot diameterin the main scanning direction is shown in FIG. 13A. Similarly, therelationship between the defocus amount and the beam spot diameter inthe sub-scanning direction is shown in FIG. 13B.

As shown in FIG. 13A, the depth clearance in the main scanning directionis 2.46 mm. As shown in FIG. 13B, the depth clearance in thesub-scanning direction is 2.58 mm. As both the depth clearances of thisembodiment are larger than 0.9 mm (based on the practical experience),the multi-beam scanning device of this embodiment ensures adequate depthclearance even when the optical scanning is performed at the writingdensity of 850 dpi, and effectively reduces the variations of the beamspots on the scanned surface to the small level so that the multi-beamscanning is carried out with accurate beam spot diameter.

The numerical aperture NAzS of this embodiment is 0.04691. It isconfirmed that the variations of the divergence angle for the respectivelight emitting parts of the semiconductor laser array are effectivelyreduced. When a photoconductive material having the exposure energy of5.5 mJ/m² is used as the photosensitive medium in this embodiment, thethreshold level of the exposure energy at the scanning speed 380.8 m/secis 4.96 mW. As the maximum output power of the laser array in thisembodiment is 8 mW, the insufficient light energy as in the conventionalmulti-beam scanning device does not occur for the present embodiment.

Next, FIG. 14 shows a configuration of the optical systems of a sixthpreferred embodiment of the multi-beam scanning device.

As shown in FIG. 14, the multi-beam scanning device of this embodimentgenerally comprises a semiconductor laser array 116, a coupling lens126, an aperture stop 136, a beam expander BX, a cylindrical lens 146, arotary polygonal mirror 156, lenses 166, 176 and 186 of the focusingoptical system, and the scanned surface 19 of the photosensitive medium.

It is a matter of course that a planer mirror may be provided at anintermediate portion of the optical path between the light source 116and the scanned surface 19 to bend the optical path in conformity withthe practical layout of the multi-beam scanning device.

In the configuration of FIG. 14, the semiconductor laser array 116 isprovided with four light emitting parts, the array pitch ρ of the lightemitting parts ρ=10 μm, the emitted laser beam wavelength 780 nm, themaximum output power 10 mW, and the inclination angle φ=81.14 degrees.

The coupling lens 126 is provided with a two-group, three-lensconfiguration, the focal length 35 mm, and the coupling function toconvert the divergent laser beams emitted by the semiconductor laserarray into less divergent laser beams.

The beam expander BX is provided between the coupling lens and therotary deflector to enlarge the diameter of the laser beams, passedthrough the coupling lens, in the main scanning direction. The beamexpander BX does not provide any beam expanding function to enlarge thediameter of the laser beams in the sub-scanning direction. Themagnification factor of the beam expander BX is 10.

The cylindrical lens 146 is provided with the focal length 149.43 mm inthe sub-scanning direction.

The aperture stop 136 is provided with the aperture width 2.04 mm in themain scanning direction and the aperture width 17.4 mm in thesub-scanning direction.

The rotary polygonal mirror 156 is provided with eight reflectionsurfaces, the inscribed circle radius 75 mm, the incident angle (betweenthe laser beam incident direction of the light source and the opticalaxis of the focusing optical system) 50 degrees, the writing density1200 dpi, and the target beam spot diameter 35 μm.

The lenses 166, 176 and 186 of the focusing optical system areconfigured as in the following table.

i Rmi Rsi X Y n Mirror Surface 0 ∞ ∞ 108.00 0.381 Lens 166 1 −126.00spherical 13.10 0 1.58201 2 ∞ 142.95 10.60 0 Lens 176 3 −2450.0spherical 22.50 0 1.49282 4 −150.00 spherical 5.60 0 Lens 186 5 ∞ ∞27.00 0 1.70400 6 −294.00 −81.10 655.10 0

In the sixth embodiment, the inclination angle φ is set to 81.14 degreesthat is near 90 degrees. The far-field pattern of this embodiment issimilar to that shown in FIG. 3D. The diameter of the laser beamsemitted from the laser array is small in the main scanning direction andlarge in the sub-scanning direction. In order to obtain an adequatelaser beam diameter needed for the main scanning direction, the couplingfunction of the coupling lens 126 is insufficient. For this reason, thebeam expander BX is provided to enlarge the diameter of the laser beamsin the main scanning direction.

In the sixth preferred embodiment, the multi-beam scanning device isconfigured to have the parameter K which is given by

K=0.82×780×10⁻³/35=0.01827.

The configuration of this embodiment meets the conditions of the aboveformula (5). In the third preferred embodiment, the multi-beam scanningdevice is configured to have the parameter

K·P/(ρ·cos φ)

which is given by $\begin{matrix}{{K \cdot {P/\left( {{\rho \cdot \cos}\quad \varphi} \right)}} = \quad {0.01827 \times {{21.167/1} \cdot \cos}\quad \left( {81.14\quad {\deg.}} \right)}} \\{= \quad {0.25108\quad.}}\end{matrix}$

The configuration of this embodiment meets the conditions of the aboveformula (9).

FIG. 15A and FIG. 15B are diagrams for explaining the relationshipbetween the defocus amount and the spot diameter in the multi-beamscanning device of FIG. 14.

In the sixth preferred embodiment, the light emitting part “ch1” of thesemiconductor laser array is positioned 12.57 μm apart from the opticalaxis of the coupling lens 126 in the sub-scanning direction. Withrespect to the defocus amount of the beam spot (which is formed on thescanned surface by the laser beam emitted from the light emitting part“ch1”) at image-height positions of nine equal subdivisions of ±150 mm,the relationship between the defocus amount and the beam spot diameterin the main scanning direction is shown in FIG. 15A. Similarly, therelationship between the defocus amount and the beam spot diameter inthe sub-scanning direction is shown in FIG. 15B.

As shown in FIG. 15A, the depth clearance in the main scanning directionis 2.22 mm. As shown in FIG. 15B, the depth clearance in thesub-scanning direction is 1.65 mm. As both the depth clearances of thisembodiment are larger than 0.9 mm (based on the practical experience),the multi-beam scanning device of this embodiment ensures adequate depthclearance even when the optical scanning is performed at the writingdensity of 1200 dpi, and effectively reduces the variations of the beamspots on the scanned surface to the small level so that the multi-beamscanning is carried out with accurate beam spot diameter.

The numerical aperture NAzS of this embodiment is 0.25108. It isconfirmed that the variations of the divergence angle for the respectivelight emitting parts of the semiconductor laser array are effectivelyreduced. When a photoconductive material having the exposure energy of4.4 mJ/m2 is used as the photosensitive medium in this embodiment, thethreshold level of the exposure energy at the scanning speed 380.8 m/secis 9.38 mW. As the maximum output power of the laser array in thisembodiment is 10 mW, the insufficient light energy as in theconventional multi-beam scanning device does not occur for the presentembodiment.

Finally, FIG. 16 shows a configuration of one preferred embodiment ofthe image forming apparatus of the present invention.

In the present embodiment, the image forming apparatus of the inventionis applied to a laser printer, and one embodiment of the multi-beamscanning device of the invention is provided in the laser printer.

As shown in FIG. 16, the laser printer 1000 includes a photoconductivedrum 1110 which is provided as the photosensitive medium that is exposedto an imaging light pattern provided by the multi-beam scanning device.At surrounding portions around the photoconductive drum 1110, a chargingroller 1121, a developing unit 1131, a transfer roller 1141, and acleaning unit 1151 are provided. A known corona charger may be used asthe charging unit 1121.

In the laser printer 1000 of FIG. 16, a multi-beam scanning device 1171according to one embodiment of the present invention is provided, and ascanned surface of the photoconductive drum 1110, which is locatedbetween the charging unit 1121 and the developing unit 1131, is exposedto multiple laser beams LB provided by the multi-beam scanning device1171.

Further, in the laser printer 1000 of FIG. 16, a fixing unit 1141, apaper cassette 1181, registration rollers 1191, a paper feeding roller1201, a transport passage 1211, ejection rollers 1221, and a paper tray1231 are provided. In the paper cassette 1181, a plurality of copysheets P are contained.

When an image forming operation is performed by the laser printer 1000,the photoconductive drum 1110 is rotated at a constant speed in aclockwise rotation direction as indicated by the arrow in FIG. 16. Thesurface of the photoconductive drum 1110 is uniformly charged by thecharging unit 1121. The charged surface of the photoconductive drum 1110is exposed to the multiple laser beams LB (the imaging light pattern)provided by the multi-beam scanning device 1171, so that anelectrostatic latent image is formed on the scanned surface of thephotoconductive drum 1110. In the present embodiment, the electrostaticlatent image is a negative latent image.

Further, the developing unit 1131 develops the latent image of thephotoconductive drum 1110 with toner, and a toned image is produced onthe scanned surface of the photoconductive drum 1110.

In the laser printer 1000, the paper cassette 1181 is removably attachedto the main body of the laser printer 1000 as shown in FIG. 16. One ofthe copy sheets P from the paper cassette 1181 is delivered to theinside of the main body by the paper feeding roller 1201. The leadingend of this copy sheet is held between the registration rollers 1191. Ata timing that is synchronous to the time the toned image of thephotoconductive drum 1110 is moved to a transferring point, theregistration rollers 1191 deliver the copy sheet through the locationbetween the transferring roller 1141 and the photoconductive drum 1110.The transferring roller 1141 electrostatically transfers the toned imagefrom the photoconductive drum 1110 to the copy sheet that is deliveredby the registration rollers 1191.

The copy sheet, after the image transferring is performed, is deliveredto the fixing unit 1161. The fixing unit 1161 performs a thermal fusingof the toner to the copy sheet. The copy sheet, after the thermal fusingis performed, is delivered through the transport passage 1211 to theejection rollers 1221. The ejection rollers 1221 delivers the copy sheetto the tray 1231 which is provided outside the main body of the laserprinter 1000. The cleaning unit 1151 performs a cleaning of the residualtoner from the surface of the photoconductive drum 1110.

In the above-described laser printer 1000, OHP (overhead projector)sheets may be used instead of the copy sheet P. Further, thetransferring of the toned image from the photoconductive drum 1110 tothe copy sheet may be performed by using an intermediate transferringmedium such as an intermediate transferring belt.

In the above-described laser printer 1000, the multi-beam scanningdevice 1171 according to the present invention can ensure adequate depthclearance when the optical scanning is performed at a high density. Themulti-beam scanning device 1171 according to the present invention iseffective in reducing the variations of the beam spots on the scannedsurface, so that the multi-beam scanning is carried out with accuratebeam spot diameter so as to create good quality of a reproduced image.Therefore, the laser printer 1000 in which the multi-beam scanningdevice 1171 of the present invention is provided can create good qualityof a reproduced image.

The present invention is not limited to the above-described embodiment,and variations and modifications may be made without departing from thescope of the present invention.

Further, the present invention is based on Japanese priority applicationNo.2000-044929, filed on Feb. 22, 2000, and Japanese priorityapplication No.2000-046368, filed on Feb. 23, 2000, the entire contentsof which are hereby incorporated by reference.

What is claimed is:
 1. A multi-beam scanning device comprising: asemiconductor laser array having a plurality of light emitting partsemitting multiple laser beams; a rotary deflector deflecting the laserbeams emitted by the light emitting parts of the semiconductor laserarray; and a focusing optical system focusing the deflected laser beamsfrom the rotary deflector onto a scanned surface to form a plurality ofbeam spots that are separated on the scanned surface in a sub-scanningdirection, the scanned surface being scanned simultaneously with theplurality of beam spots in a main scanning direction by a rotation ofthe rotary deflector, wherein the laser array is configured such thatthe light emitting parts are arrayed along a line that is at aninclination angle φ to the sub-scanning direction, the inclination angleφ measured in degrees and meeting the conditions 0≦φ<90, and that ascanning line pitch P, an array pitch ρ of the light emitting parts ofthe laser array and a parameter K defined by the equation K=0.82λ/ωz, where λ is a wavelength of the emitted laser beams and ωz is a targetbeam spot diameter in the sub-scanning direction, satisfy the followingconditions:  0.01<K·P/(ρ·cos φ)<0.30 0.011<K<0.030.
 2. The multi-beamscanning device of claim 1 further comprising: a coupling lens couplingthe laser beams emitted by the laser array; an aperture stop restrictinga diameter of the laser beams passed through the coupling lens; and aline focusing lens providing a refraction power to the laser beams,passed through the aperture stop, with respect to only the sub-scanningdirection, the rotary deflector having reflection surfaces, the rotarydeflector deflecting the laser beams from the laser array by one of thereflection surfaces, and the focusing optical system focusing thedeflected laser beams from the rotary deflector onto the scanned surfaceto form the beam spots thereon.
 3. The multi-beam scanning device ofclaim 1 wherein the semiconductor laser array is configured such thatthe inclination angle of the light emitting parts is equal to
 0. 4. Themulti-beam scanning device of claim 1 wherein the semiconductor laserarray is configured such that the inclination angle of the lightemitting parts is larger than
 0. 5. The multi-beam scanning device ofclaim 2 wherein the coupling lens is configured to convert the laserbeams emitted by the semiconductor laser array into parallel laserbeams.
 6. The multi-beam scanning device of claim 2 wherein the lightemitting parts of the semiconductor laser array emit divergent laserbeams, and the coupling lens is configured to convert the laser beamsemitted by the semiconductor laser array into less divergent laserbeams.
 7. The multi-beam scanning device of claim 2 wherein the rotarydeflector comprises a rotary polygonal mirror, the rotary polygonalmirror being rotated at a constant speed around a rotation axis of therotary polygonal mirror, which allows the scanned surface to be scannedat a constant speed in the main scanning direction with the beam spots.8. The multi-beam scanning device of claim 5 wherein the rotarydeflector comprises a rotary polygonal mirror and the focusing opticalsystem comprises an fθ lens.
 9. The multi-beam scanning device of claim2 wherein the line focusing lens comprises a cylindrical lens.
 10. Themulti-beam scanning device of claim 4 wherein the semiconductor laserarray is configured such that the inclination angle of the lightemitting parts is larger than 0 and approximately equal to 90, themulti-beam scanning device further comprising a main-scanning-directionbeam expander provided between the coupling lens and the rotarydeflector, the beam expander enlarging the diameter of the laser beams,passed through the coupling lens, in the main scanning direction.
 11. Alight source device for use in a multi-beam scanning device, the lightsource device comprising: a semiconductor laser array having a pluralityof light emitting parts emitting multiple laser beams; a coupling lenscoupling the laser beams emitted by the laser array; and an aperturestop restricting a diameter of the laser beams passed through thecoupling lens, wherein the multi-beam scanning device comprising: thelight source device; a rotary deflector deflecting the laser beamsemitted by the light emitting parts of the laser array; and a focusingoptical system focusing the deflected laser beams from the rotarydeflector onto a scanned surface to form a plurality of beam spots thatare separated on the scanned surface in a sub-scanning direction, thescanned surface being scanned simultaneously with the plurality of beamspots in a main scanning direction by a rotation of the rotarydeflector, wherein the laser array is configured such that the lightemitting parts are arrayed along a line that is at an inclination angleφ to the sub-scanning direction, the inclination angle φ measured indegrees and meeting the condition 0≦φ<90, and that a scanning line pitchP, an array pitch ρ of the light emitting parts of the laser array and aparameter K defined by the equation K=0.82λ/ωz,  where λ is a wavelengthof the emitted laser beams and ωz is a target beam spot diameter in thesub-scanning direction, satisfy the following conditions:0.01<K·P/(ρ·cos φ)<0.30 0.011<K<0.030  and wherein the aperture stop isconfigured to have a numerical aperture NAzS in the sub-scanningdirection that satisfies the conditions: 0.01<NAzS<0.30.
 12. The lightsource device of claim 11 wherein the semiconductor laser array isconfigured such that the inclination angle of the light emitting partsis equal to
 0. 13. The light source device of claim 11 wherein thesemiconductor laser array is configured such that the inclination angleφ of the light emitting parts is larger than
 0. 14. The light sourcedevice of claim 11 wherein the coupling lens is configured to convertthe laser beams emitted by the semiconductor laser array into parallellaser beams.
 15. The light source device of claim 14 wherein thecoupling lens comprises a single lens.
 16. The light source device ofclaim 11 wherein the light emitting parts of the semiconductor laserarray emit divergent laser beams, and the coupling lens is configured toconvert the laser beams emitted by the semiconductor laser array intoless divergent laser beams.
 17. The light source device of claim 11wherein the semiconductor laser array is configured such that the arraypitch ρ of the light emitting parts is equal to 10 μm.
 18. The lightsource device of claim 11 wherein the semiconductor laser array isconfigured such that the wavelength λ of the emitted laser beams isbelow 700 nm.
 19. A multi-beam scanning method comprising the steps of:providing a semiconductor laser array having a plurality of lightemitting parts emitting multiple laser beams; providing a rotarydeflector deflecting the laser beams emitted by the light emitting partsof the semiconductor laser array; focusing the deflected laser beamsfrom the rotary deflector onto a scanned surface to form a plurality ofbeam spots that are separated on the scanned surface in a sub-scanningdirection; and scanning the scanned surface simultaneously with theplurality of beam spots in a main scanning direction by a rotation ofthe rotary deflector; wherein the laser array is configured such thatthe light emitting parts are arrayed along a line that is at aninclination angle φ to the sub-scanning direction, the inclination angleφ measured in degrees and meeting the conditions 0≦φ<90, and that ascanning line pitch P, an array pitch ρ of the light emitting parts ofthe laser array and a parameter K defined by the equation K=0.82λ/ωz, where λ is a wavelength of the emitted laser beams and ωz is a targetbeam spot diameter in the sub-scanning direction, satisfy the followingconditions: 0.01<K·P/(ρ·cos φ)<0.30 0.011<K<0.030.
 20. An image formingapparatus in which a multi-beam scanning device is provided, the imageforming apparatus forming an electrostatic latent image on a scannedsurface of a photosensitive medium through an exposure of thephotosensitive medium to an imaging light pattern provided by themulti-beam scanning device, the multi-beam scanning device comprising: asemiconductor laser array having a plurality of light emitting partsemitting multiple laser beams; a rotary deflector deflecting the laserbeams emitted by the light emitting parts of the semiconductor laserarray; and a focusing optical system focusing the deflected laser beamsfrom the rotary deflector onto a scanned surface to form a plurality ofbeam spots that are separated on the scanned surface in a sub-scanningdirection, the scanned surface being scanned simultaneously with theplurality of beam spots in a main scanning direction by a rotation ofthe rotary deflector, wherein the laser array is configured such thatthe light emitting parts are arrayed along a line that is at aninclination angle φ to the sub-scanning direction, the inclination angleφ measured in degrees and meeting the conditions 0≦φ<90, and that ascanning line pitch P, an array pitch ρ of the light emitting parts ofthe laser array and a parameter K defined by the equation K=0.82λ/ωz, where λ is a wavelength of the emitted laser beams and ωz is a targetbeam spot diameter in the sub-scanning direction, satisfy the followingconditions: 0.01<K·P/(ρ·cos φ)<0.30  0.011<K<0.030.
 21. The imageforming apparatus of claim 20 wherein the photosensitive medium is aphotoconductive drum, and the image forming apparatus uniformly chargesthe photoconductive drum and exposes the photoconductive drum to theimaging light pattern provided by the multi-beam scanning device, sothat the electrostatic latent image is formed on the scanned surface ofthe photoconductive drum, and the image forming apparatus developing thelatent image of the photoconductive drum with toner and transferring atoned image from the photoconductive drum to a copy sheet.
 22. Amulti-beam scanning device comprising: semiconductor laser array meanshaving a plurality of light emitting parts for emitting multiple laserbeams; rotary deflector means for deflecting the laser beams emitted bythe light emitting parts of the laser array means; and focusing opticalmeans for focusing the deflected laser beams from the rotary deflectormeans onto a scanned surface to form a plurality of beam spots that areseparated on the scanned surface in a sub-scanning direction, thescanned surface being scanned simultaneously with the plurality of beamspots in a main scanning direction by a rotation of the rotary deflectormeans, wherein the laser array means is configured such that the lightemitting parts are arrayed along a line that is at an inclination angleφ to the sub-scanning direction, the inclination angle φ measured indegrees and meeting the conditions 0≦φ<90, and that a scanning linepitch P, an array pitch ρ of the light emitting parts of the laser arraymeans and a parameter K defined by the equation K=0.82λ/ωz,  where λ isa wavelength of the emitted laser beams and ωz is a target beam spotdiameter in the sub-scanning direction, satisfy the followingconditions: 0.01<K·P/(ρ·cos φ)<0.30 0.011<K<0.030.